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A one-dimensional tapered fin element has the nodal coordinates x; = 20 mm and x; = 60 mm with the area of cross section changing linearly from a value of A; = 20 mmat x; to a value of A;= 10 mm? at x; as shown in Figure 3.7. (1) Determine the matrix of shape functions and (2) express the area k3 of cross section of the fin element in terms of the shape functions. Approach: (1) Use the shape functions corresponding to linear variation of the field variable. (2) Express linear variation of cross-sectional area in terms of shape functions similar to the variation of the field variable. A one-dimensional tapered fin element has the nodal coordinates x; = 20 mm and x; = 60 mm with the area of cross section changing linearly from a value of A; = 20 mmat x; to a value of A;= 10 mm? at x; as shown in Figure 3.7. (1) Determine the matrix of shape functions and (2) express the area k3 of cross section of the fin element in terms of the shape functions. Approach: (1) Use the shape functions corresponding to linear variation of the field variable. (2) Express linear variation of cross-sectional area in terms of shape functions similar to the variation of the field variable